a
Using Accelerometers in Low
g
Applications
by Charles Kitchin
AN-374
APPLICATION NOTE
ONE TECHNOLOGY WAY
•
P.O. BOX 9106
•
NORWOOD, MASSACHUSETTS 02062-9106
•
617/329-4700
INTRODUCTION
Accelerometers can be used in a wide variety of low
g
applications such as tilt and orientation, vibration analy-
sis, motion detection, etc. This application note explains
how to best apply the ADXL50 (50
g
) and ADXL05 (5
g
)
accelerometers when measuring signals at the low end
of their respective full-scale ranges. Although each
accelerometer is specified according to its full scale
(clipping)
g
level, the limiting resolution of the device,
i.e., its minimum discernible input level, is extremely im-
portant when measuring low
g
accelerations.
The limiting resolution is predominantly set by the mea-
surement noise “floor” which includes the ambient
background noise and the noise of the accelerometer it-
self. The level of the noise floor varies directly with the
bandwidth of the measurement. As the measurement
bandwidth is reduced, the noise floor drops, improving
the signal-to-noise ratio of the measurement and its
limiting resolution.
DEVICE BANDWIDTH VS. MEASUREMENT RESOLUTION
The output noise of the ADXL50 and ADXL05 scales
with the square root of the measurement bandwidth.
The maximum amplitude of the noise, its peak-to-peak
value, approximately defines the worst-case resolution
of a measurement. The peak-to-peak noise is approxi-
mately equal to 6.6 times its rms value (for an average
uncertainty of 0.1%).
The bandwidth of the accelerometer can be easily re-
duced by adding low-pass or bandpass filtering. Figure
1 shows the noise vs. bandwidth characteristics of the
ADXL50 and ADXL05 devices.
As shown by the figure, device noise drops dramatically
as the operating bandwidth is reduced. For
example, when operated in a 1 kHz bandwidth, the
ADXL05 typically has a peak-to-peak noise level of
130 m
g
. With ±5
g
applied accelerations, this 130 m
g
resolution limit is normally quite satisfactory; but for
1.5
g
150m
g
15m
g
1.5m
g
150µ
g
3dB BANDWIDTH – Hz
NOISE LEVEL – Peak to Peak
NOISE LEVEL – rms
10
g
1m
g
10m
g
100m
g
1
g
10 100 1k
ADXL05
ADXL50
Figure 1. Noise Level vs. 3 dB Bandwidth
–2–
smaller acceleration levels the noise is now a much
greater percentage of the signal. As shown by Figure 1,
when the device bandwidth is rolled off to 100 Hz, the
peak-to-peak noise level is reduced to approximately
40 m
g
, and at 10 Hz it is down to 10 m
g
.
Alternatively, the signal-to-noise ratio may be improved
considerably by using a microprocessor to perform
multiple measurements and then compute the average
signal level. When using this technique, the signal level
will be increased directly with the number of measure-
ments while the noise will only increase by their square
root. For example, with 100 measurements, the signal-to-
noise ratio will be increased by a factor of 10 (20 dB).
Low-Pass Filtering
The bandwidth of either accelerometer can be reduced by
providing post filtering. Figure 2 shows how the buffer
amplifier can be connected to provide 1-pole post filtering,
0
g
offset trimming, and output scaling. Two tables are in-
cluded with the figure which provide practical component
values for various full-scale
g
levels and approximate cir-
cuit bandwidths. For bandwidths other than those listed,
use the formula:
Capacitor C4 (Farads) = 1
2 π×R3(Ω)×3dB BW (Hz)
or simply scale the value of capacitor C4 accordingly, i.e.,
for an application with a 50 Hz bandwidth, the value of C4
will need to be twice as large as its 100 Hz value. If further
noise reduction is needed while maintaining the maxi-
mum possible bandwidth, then a 2- or 3-pole post filter is
recommended. These provide a much steeper roll-off of
noise above the pole frequency. Figure 3 shows a circuit
that uses the buffer amplifier to provide 2-pole post filter-
ing. Component values for the 2-pole filter were selected
to operate the buffer at unity gain.
FULL
SCALE mV
per
g
3dB
BW (Hz) R1a
kΩR2
kΩ
100
100
100
100
C4
µF
R3
kΩ
200
100
200
100
±10
g
±20
g
±10
g
±20
g
100
100
10
10
5
5
5
5
21.5
23.7
21.5
23.7
249
137
249
137
0.0068
0.01
0.068
0.01
R1b
kΩ
3dB BW = 1
2π R3 C4
ADXL50 COMPONENT VALUES FOR VARIOUS
FULL-SCALE RANGES AND BANDWIDTHS
BUFFER
AMP
ADXL50 OR ADXL05
V
PR
+3.4V
REF V
IN–
C4
V
OUT
1.8V
PRE-AMP
+5V
R1a R3
0
g
LEVEL
TRIM 50kΩ
R1b
OPTIONAL SCALE
FACTOR TRIM*
R2
0.1µF
COM
0.022µF
0.022µF
C2
C1
C1
*TO OMIT THE OPTIONAL SCALE FACTOR
TRIM , REPLACE R1a AND R1b WITH A
FIXED VALUE 1% METAL FILM RESISTOR.
SEE VALUES SPECIFIED IN TABLES BELOW.
4
2
3
5
6810
9
1
ADXL05 COMPONENT VALUES FOR VARIOUS
FULL-SCALE RANGES AND BANDWIDTHS
100
100
100
100
2000
1000
500
400
±1
g
±2
g
±4
g
±5
g
10
100
200
300
10
10
10
10
24.9
35.7
35.7
45.3
301
200
100
100
0.056
0.0082
0.0082
0.0056
FULL
SCALE mV
per
g
3dB
BW (Hz) R1a
kΩR2
kΩC4
µF
R3
kΩ
R1b
kΩ
3dB BW = 1
2π R3 C4
Figure 2. Using the Buffer Amplifier to Provide 1-Pole Post Filtering Plus Scale Factor and 0 g Level Trimming
–3–
Capacitors C3 and C4 were chosen to provide 3 dB band-
widths of 10 Hz, 30 Hz, 100 Hz, and 300 Hz.
In this configuration, the nominal buffer amplifier out-
put will be +1.8 V ± the scale factor of the accelerometer,
either 19 mV/
g
for the ADXL50 or 200 mV/
g
for the
ADXL05. An AD820 external op amp allows
noninteractive adjustment of 0
g
offset and scale factor.
The external op amp offsets and scales the output to
provide a +2.5 V ± 2 V output over a wide range of full-
scale
g
levels.
Additional Noise Reduction Techniques
In addition to reducing circuit noise, any electro-
magnetic interference (EMI) needs to be considered.
Shielded wire should be used for connecting the accel-
erometer to any equipment or circuitry that is more than
a few inches away. A common problem is that of 60 Hz
pickup from ac line voltage. This can be minimized by
physically moving the device away from power leads, or
if that is not practical, using proper shielding and
grounding techniques. In most cases, it is advisable to
ground the cable’s shield at only one end and connect a
separate common lead between the circuits; this will
help to prevent ground loops. Also, if the accelerometer
is inside or near a metal enclosure, this should be
grounded as well.
Another area to consider is mechanical resonance of the
overall measurement system. The use of a highly flexi-
ble shielded wire will greatly help to prevent secondary
resonance effects of wire vibrating at its natural fre-
quency. A shielded cable with a silicone jacket and sili-
cone insulation such as that produced by Cooner Wire
Company of Chatsworth, California, is recommended.
2-POLE FILTER
COMPONENT VALUES
3dB
BW (Hz) C4µF
0.027
0.082
0.27
0.82
300
100
30
10
0.0033
0.01
0.033
0.1
C3µF
BUFFER
AMP
ADXL50
OR
ADXL05
V
PR
V
REF
9
10
8
OPTIONAL CAPACITOR
FOR 3-POLE FILTERING
R4b
V
IN
–
C4
V
OUT
+5V
1.8V
OUTPUT
0
g
LEVEL
TRIM
PRE-AMP
R5
42.2kΩ
C3
R4a
R1
82.5kΩR3
82.5kΩSCALE
FACTOR
TRIM
R6
40.2kΩ
20kΩ
R7
71.5kΩ
6
7
4
2
3
0.01µF
OFFSET AND
SCALING
AMPLIFIER
R5
AD820
2-POLE FILTER
+3.4V
6
ADXL05 OFFSET AND SCALING
AMPLIFIER COMPONENT VALUES
FULL
SCALE mV per
g
R4a
kΩR5
kΩ
2000
1000
500
400
±1
g
±2
g
±4
g
±5
g
10.00
4.98
2.50
2.00
10
10
10
10
24.9
35.7
35.7
45.3
301
200
100
100
R4b
kΩ
GAIN
ADXL50 OFFSET AND SCALING
AMPLIFIER COMPONENT VALUES
MAX
INPUT R4a
kΩR5
kΩ
±10
g
±20
g
200
100
10.53
5.26
5
5
21.5
23.7
249
137
R4b
kΩ
GAIN
SCALE
FACTOR IN
mV/
g
Figure 3. Two-Pole Filtering Circuit with Gain and 0 g Offset Adjustment
–4–
OFFSET DRIFT CONSIDERATIONS
When using an accelerometer with a dc (gravity sensing)
response, the 0
g
offset level will exhibit some tempera-
ture drift. When the accelerometer must measure low
g
levels over wide temperature ranges, the 0
g
drift can be-
come large in proportion to the signal amplitude. If a dc
response is truly needed, there are a number of design
options available. One very straightforward approach is to
use a low cost crystal oven to maintain the accelerometer
at a constant temperature. These ovens are particularly
useful in high accuracy tilt applications. After the circuit
has been built and is operating correctly, the crystal oven
can be mounted over the accelerometer and powered off
the same +5 V power supply. Figure 4 shows the basic circuit.
The ovens may be purchased from Isotemp Research, Inc.,
P.O. Box 3389, Charlottesville, VA 22903, phone 804-295-
3101. For more details on crystal oven compensation, re-
fer to application note AN-385.
Other methods for 0
g
drift compensation include using a
low cost temperature sensor such as the AD590 to supply
a microprocessor with the device temperature. If the drift
curve of the accelerometer is stored in the µP, then a soft-
ware program can be used to subtract out the drift. This
method works well, removing both the linear and nonlin-
ear components of the drift. But due to device-to-device
variation, it requires that the drift curve of each individual
accelerometer be known (or measured). Alternatively,
various drift compensation circuits can be used to subtract
out the
linear portion
of
the accelerometer’s drift by using
a temperature sensor and op amp to supply a small com-
pensation current. This hardware approach does not use a
µP but does require calibrating the compensation circuitry
for each device. For more details on software and hard-
ware drift compensation, refer to application note AN-380.
ISOTEMP
M050570
+5V
1
2
3
+VDC
NC
0VDC
BUFFER
AMP
ADXL50
OR
ADXL05
V
PR
+3.4V
REF
V
IN–
C
F
COM
V
OUT
0.022µF
0.022 µF
R3
+5V
1.8V
C1
C3
0.1µF
PRE-AMP
R1
6
V
OUT
C1
C2
0
g
OUTPUT – +2.5V
3dB Bw – 1Hz
8
9
1
3
2
4
5
10
V
PR
DEVICE FS MEASUREMENT
RANGE* OUTPUT
SENSITIVITY BUFFER
GAIN R1 R3 C
F
ADXL50
ADXL05
100mV/
g
500mV/
g
5.26
2.50
26.1k
40.2k
137k
100k
1µF
1.5µF
*FS RANGE NUMBERS ARE CONSERVATIVE TO ALLOW FOR V
PR
0
g
TOLERANCE.
±10
g
±2
g
Figure 4. Low g DC Coupled (Tilt) Circuit Using Crystal Oven Compensation
–5–
AC Coupling
If a dc (gravity) response is not required—for example in
motion sensing or vibration measurement applica-
tions—ac coupling can be used between the preampli-
fier output and the buffer input as shown in Figure 5.
Because ac coupling removes the dc component of the
output, the preamp output signal may be amplified con-
siderably without increasing the 0
g
level drift. If capaci-
tor C5 is added to the ac coupling circuit, forming a
1-pole low-pass filter, then a bandpass function is pro-
vided that will attenuate any signals other than those
within the pass band. A typical ac coupled frequency re-
sponse is shown in Figure 6.
The low frequency roll-off, FL, due to the ac coupling net-
work is:
F
L
=1
2π
R
1
C
4
In this case, the high frequency roll-off, FH, is determined
by the 1-pole post filter R3, C5.
If ac coupling is used, the self-test feature must be moni-
tored at VPR, rather than at the buffer output (since the
self test output is a dc voltage).
20
10
0
–10
–20
0.1 1 10 100 1k
FREQUENCY – Hz
–30
NORMALIZED OUTPUT LEVEL – dB
LOW FREQUENCY ROLL-OFF ( F
L
)
HIGH FREQUENCY ROLL-OFF ( F
H
)
Figure 6. Typical Output vs. Frequency Curve when AC
Coupling V
PR
to the Buffer
Note that capacitor C4 should be a nonpolarized, low
leakage type. If a polarized capacitor is used, tantalum
types are preferred, rather than electrolytic. With polar-
ized capacitors, VPR should be measured on each device
and the positive terminal of the capacitor connected to-
ward either VPR or VIN—whichever is more positive.
0.002µF
0.0039µF
0.0068µF
0.01µF
0.068µF
200
100
200
100
200
30
10
3
1
0.1
24
24
24
24
24
0.22µF
0.68µF
2.2µF
6.8µF
68µF
300
300
100
100
10
249
127
249
127
249
640kΩ
326kΩ
640kΩ
326kΩ
640kΩ
SCALE
FACTOR
IN
mV/
g
DESIRED
LOW
FREQUENCY
LIMIT, FL
R1
VALUE
IN kΩ
CLOSEST
C4
VALUE
DESIRED
HIGH
FREQUENCY
LIMIT, FHR3
IN kΩ
CLOSEST
C5
VALUE
VALUE
OF R2
FOR +2.5V
0
g
LEVEL
ADXL50
0.002µF
0.002µF
0.0068µF
0.0068µF
0.068µF
1000
200
1000
200
200
30
30
3
1
0.1
49.9
249
49.9
249
249
0.10µF
0.022µF
1.0µF
0.68µF
6.8µF
249
249
249
249
249
640kΩ
640kΩ
640kΩ
640kΩ
640kΩ
300
300
100
100
10
SCALE
FACTOR
IN
mV/
g
DESIRED
LOW
FREQUENCY
LIMIT, FL
R1
VALUE
IN kΩ
CLOSEST
C4
VALUE
DESIRED
HIGH
FREQUENCY
LIMIT, FHR3
IN kΩ
CLOSEST
C5
VALUE
VALUE
OF R2
FOR +2.5V
0
g
LEVEL
ADXL05
BUFFER
AMP
ADXL50 OR ADXL05
V
PR
V
IN–
C5
V
OUT
R3
1.8V
PRE-AMP
R1
R2
V
PR 9
10
8
C4
COMPONENT
VALUES ARE
APPROXIMATE.
FOR MAXIMUM
ACCURACY,
SCALE FACTOR
TRIMMING SHOULD BE
EMPLOYED.
Figure 5. AC Coupling the V
PR
Output to the Buffer Input
–6–
E2007–9–3/95
PRINTED IN U.S.A.
GAIN SELECTION ISSUES
The uncommitted amplifier incorporated into the ADXL50
and ADXL05 devices allows the user to readily set the
scale factor to the desired voltage output per
g
of applied
acceleration. However, some caution is advised in not set-
ting the scale factor, too high as the output buffer could
run out of “headroom,” i.e., the buffer’s output can go as
low as 0.25 volts and as high as 4.75 volts. This means the
buffer’s maximum output swing is +2.5 V ± 2.25 V. If the
gain is too high, the buffer can clip on periodic transient
accelerations; or it can clip due to the fact that the 0
g
off-
set drift is also amplified along with the signal.
Therefore, use only enough gain in the buffer as is neces-
sary to override any transmission losses between the ac-
celerometer and any following circuitry (i.e., to keep the
system’s signal to noise ratio high).
Using the Earth’s Gravity to Calibrate the Accelerometer
Both the 0
g
offset and scale factor of the ADXL50 and
ADXL05 devices may be roughly calibrated by using the
1
g
(average) acceleration of the Earth’s gravity. Figure 7
shows how gravity and package orientation affect the out-
put polarity. Note that the output polarity is that which ap-
pears at VPR; the output at VOUT will have the opposite sign
(due to the buffer amplifier’s inverting configuration).
With its axis of sensitivity in the vertical plane, the acceler-
ometer should register a 1
g
acceleration, either positive
or negative, depending on orientation. With the axis of
sensitivity in the horizontal plane, no acceleration (0
g
)
should be indicated.
Calibrate the accelerometer by placing it on its side with
its axis of sensitivity oriented as shown in “a.” The 0
g
offset potentiometer, RT, (as shown in Figure 2) is then
roughly adjusted for midscale: +2.5 V at the buffer output.
0
g
(a) 0
g
(b) –1
g
(c) +1
g
(d)
INDICATED POLARITY IS THAT
OCCURING AT V
PR
Figure 7. Using the Earth’s Gravity to Calibrate the
ADXL50 and ADXL05 Accelerometers
If the optional scale factor trimmer, R1a, is to be used, it
should be adjusted next. The package axis should be ori-
ented as in “c” (pointing down) and the output reading
noted. The package axis should then be rotated 180° to
position “d” and R1a adjusted so that the output voltage
indicates a change of 2
g
s in acceleration. For example, if
the circuit scale factor at the buffer output is 200 mV per
g
,
then the scale factor trim should be adjusted so that an
output change of 400 mV is indicated.
Adjusting the circuit’s scale factor will have some effect
on its 0
g
level, so this should be readjusted, as before, but
this time checked in both positions “a” and “b.” If there is
a difference in the 0
g
reading, a compromise should be
selected so that the reading in each direction is equal dis-
tant from +2.5 V. Scale factor and 0
g
offset adjustments
should be repeated until both are correct.
APPLICATIONS ASSISTANCE
For applications assistance contact Charles Kitchin,
Accelerometer Applications, Analog Devices Semicon-
ductor, 831 Woburn St., Wilmington, MA 01887. Phone:
617-937-1665.